Sensor arrays are used in many application fields including RADAR, SONAR, geophysics, telecommunications and medical imaging. For these applications, the received data is often processed using so-called conventional “delay-and-sum” beamforming to localize source or target locations. While this approach is straightforward and easy to implement, off-axis scatters, known as jammers in the RADAR/SONAR literature, can introduce clutter, reducing the overall quality of the beamformer output. This is shown schematically and with actual and simulated images formed using delay and sum beamforming processing, by comparing FIGS. 1A-1C. In FIGS. 1A-1C, an array 10 of sensors 12 is focused along an axis 1 in a direction indicated by the arrow that is often referred to as the “look direction”. In FIG. 1A, a single target (“single point” target) has been placed along the look direction, on axis 1 at a fixed distance from array 10. As the target 2 either emits or reflects energy toward the array 10, a signal is received by each of the individual sensors 12. Focal delays (T1-T3) are applied to each signal received, corresponding to the relative distances of the respective sensors from axis 1 and as a function of the distance of target 2 from array 10, from which the sensor/range set of data 6 is produced as shown in the image portion of FIG. 1A. Summation across sensors 12 to form an image line amplifies the signal coming from the look direction.
However, when a secondary target 2′ is placed off-axis, as shown in FIG. 1B, it may lie within the array's beam and energy emitted or reflected from target 2′ toward array 10 may contribute to corrupt the desired image information from target 2. This is represented by the tilted waveforms 7 visible in the sensor/range data set image shown in FIG. 1B. Although summation across sensors would amplify the signal coming from directly in front of the array 10, it would not entirely eliminate the contribution of the off-axis target 2′.
FIG. 1C shows an image of medical ultrasound data obtained from the thyroid of a human subject. At least three clear waveforms 6, 7 and 8 are visible in this sensors/range data set image. Thus, non-focal targets appear in this image line as clutter, reducing image contrast, and reducing clarity of the image 6 of the on-axis target that is desired to be visualized. FIG. 1C shows focused single channel radio frequency (RF) echo data obtained from the thyroid of a human subject at Duke University, United States of America. The vertical axis represents channel number (sensor), while the horizontal axis represents arrival times of the signals. Although summation across channels (i.e., conventional beamforming) to form an RF image line would amplify the echo 6 coming from directly in front of the array, it would not entirely eliminate the two other visible targets 7 and 8. These non-focal targets would appear in this image line as clutter, reducing image contrast. In addition to the three dominant waveforms 6, 7 and 8 the data set also includes echoes from background speckle. These background echoes also include discernable off-axis scatterers that generate further clutter in the image. The successful application of adaptive beamforming to medical ultrasound would reduce the effects of bright off-axis targets, thus improving the overall image quality.
The problem of nullifying the contribution of jammers was first investigated for RADAR and SONAR systems by extending the pioneering work of Norbert Wiener. The application of Wiener filter theory to array signal processing led to the initial development of adaptive beamforming [1-3]. In adaptive beamforming, the information associated with the data received by an array of sensors is used to determine a set of weights that optimize the beamformer output.
In the past fifty years, a plethora of algorithms have been developed, each exploiting specific properties of the received data. These algorithms are able to achieve resolution far superior to that predicted by diffraction theory, while attaining excellent side lobe reduction (i.e., image contrast). The most common approaches calculate the weights by minimizing the energy in the beamsum signal, subject to the constraint that the beamformer must exhibit a given response in the look-direction [4, 5]. Typically, the second order statistics (i.e., the covariance matrix) of the data are used to generate the weights. These algorithms were initially applied in passive SONAR, where the use of receive only systems allowed one to obtain numerous unique statistical looks at the environment. This is not generally the case for a transmit/receive system, such as those employed in medical ultrasound.
In parallel with the development of these “statistical beamformers”, alternative algorithms were also developed which utilized different properties of the received signals. Common approaches include the reduced rank beamformers [6-8]. The basic concept underlying these methods is to save computation time by calculating a reduced rank covariance matrix that only includes the strongest jammers. Oblique projections have also been proposed to beamform the data in a signal space which is orthogonal to the signal space spanned by the jammers [9, 11].
It is often the case that limited data are available, making computation of a reliable covariance matrix difficult. This could be due, for example, to non-stationary environments, fast moving targets, or the application of transmit/receive systems. In these cases, several groups have proposed the use of a diagonal loading term to obtain a stable covariance matrix which allows solution for the optimal weights [12-15]. Diagonal loading is a common technique in array signal processing to stabilize a matrix ill-conditioned for inversion. Along with these so-called “regularization approaches”, a series of adaptive algorithms has also been developed which do not rely on statistical properties of the data and thus can be used on a single realization (or snapshot). These approaches are particularly well suited to pulse-echo imaging. These algorithms include techniques based on generalized eigenvalue problems [16, 17], Bayesian approaches [18-20], maximum likelihood estimators [21, 22], data-adaptive regularization [23], and minimum worst-case gain methods [24]. The Spatial Processing Optimized and Constrained (SPOC) algorithm was first described by Van Trees et al. in [18] for applications in passive SONAR systems, assuming narrow-band signals received from the far-field. In passive SONAR the received data x is simply an N element vector of the complex demodulated signals received on each channel. Since passive SONAR assumes narrow-band signals, this received data consists of only a single complex sample on each channel. Thus, the signals, originating from the far-field, are assumed to be received in a linear progression of arrival times. Further, the narrow band nature of the analysis involves the selection of a single frequency of signals to be processed. The signal from a single far-field target received by a uniformly spaced linear array takes on the form of a discretely sampled complex exponential. The array manifold matrix for this application thus consists of a set of Q columns, each of which is an N sample complex exponential of a different frequency (Q is the number of hypothetical sources placed in the far-field).
In medical ultrasound, bright off-axis targets can seriously degrade image quality by introducing broad image clutter, which reduces image contrast and resolution. It is well known that the acoustic reflectivity of targets within the body covers many orders of magnitude [25]. The unique characteristics of ultrasound data make blind application of existing adaptive beamforming algorithms unlikely to be successful. Unlike passive SONAR, for example, limited statistics are available in medical ultrasound to form a robust covariance matrix. This is particularly pronounced when the target includes non-stationary environments, such as is often the case when attempting to view living tissue. Furthermore, on-axis and off-axis signals are strongly correlated, requiring the use of special algorithms such as the Duvall beamformer [26] or pre-processing techniques such as spatial smoothing to decorrelate signals before filtering is applied [27-31]. Lastly, ultrasound imaging is generally performed using broad-band signals in the near-field, while many adaptive beamforming techniques are specifically designed for narrow-band signals in the far-field.
In the past, several groups have applied adaptive algorithms to medical ultrasound beamforming Mann and Walker [32, 33] showed an increased resolution and contrast using a modified version of the Frost beamformer [5]. Other groups [34, 35] have applied the Capon beamformer [4] coupled with spatial smoothing to decorrelate on-axis and off-axis signals. Synthetic transmit focusing was used in these approaches to generate a robust covariance matrix. Although initial results are positive, the use of synthetic transmit poses significant limits on the application of these algorithms in real clinical environments because of potential motion artifacts and limitations of existing hardware.
Most adaptive beamforming algorithms, such as those previously described, tend to fail when applied to medical ultrasound data. Failure can be attributed to one or more of the following factors: the medical ultrasound data is procured in a near-field scenario; the signals obtained that make up the medical ultrasound data are broadband; and there is limited statistical information available, as noted. Medical ultrasound data is naturally processed in the time domain, and thus, existing algorithms require an extra step of selecting single frequency data for such processing.
Thus, there remains a need for systems and methods of improving medical ultrasonic imaging to reduce clutter in the resulting image to form a clearer image of the intended target. It would further be desirable and more natural to process medical ultrasonic image data as time-domain signals to thereby take advantage of the temporal coherence available in the data. Further, and more generally, there remains a need for systems and methods of improving imaging of signals received from near-field and/or broadband targets, as well as methods and system of localizing sources of such targets.